Combine the sugar and vinegar in a small saucepan. Cook, stirring constantly, over medium heat until the sugar completely dissolves, 3 to 5 minutes. Remove from the heat and cool, the mixture should be the consistency of maple syrup.
Combine the strawberries and basil in a food processor and puree. Add the sugar mixture and pulse the machine to combine. Pour into an 8-inch square baking dish, cover loosely with plastic wrap and freeze for about 2 hours.
When the edges begin to harden, use the tines of a fork to scrape them into bits. Repeat the procedure in 1 to 2 hours, and then occasionally thereafter, until the mixture is frozen through in "shavings." Freeze overnight.
Spoon the granita into serving dishes and garnish each with a basil leaf, then serve.
Adjust the amount of sugar based on the sweetness of the strawberries.
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